Inequality word problems
- 2. Additional Example 3: Money Application Edgar’s August profit of $137 was at least $20 higher than his July profit. What was July’s profit? Let p represent the profit increase from July to August. August profit was at least $20 higher than July’s profit. $137 ≥ 20 + p 137 ≥ 20 + p Subtract 20 from both sides. -20 -20 117 ≥ p p ≤ 117 Rewrite the inequality. July’s profit was at most $117.
- 3. Check It Out: Example 3 Rylan’s March profit of $172 was at least $12 less than his February profit. What was February’s profit? Let p represent the profit decrease from February to march. March profit was at least $12 less than February’s profit. $172 ≥ -12 + p 172 ≥ -12 + p Add 12 to both sides. +12 +12 184 ≥ p p ≤ 184 Rewrite the inequality. February’s profit was at most $184.
- 4. Friday’s high temperature was 20 °F. Saturday’s high temperature was forecast to be no more than 8 °F warmer than Friday’s high temperature. According to the forecast, what are the possible high temperatures for Saturday? X < 28
- 5. In order for a field trip to be scheduled, at least 30 students must sign up. So far, 23 students have signed up. At least how many more students must sign up in order for the field trip to be scheduled? X + 23 > 30 -23 -23 x > 7
- 6. Additional Example 3: Application It cost Josh $85 to make candles for the craft fair. How many candles must he sell at $4.00 each to make a profit? Since profit is the amount earned minus the amount spent, Josh needs to earn more than $85. Let c represent the number of candles that must be sold. 4c > 85 Write an inequality. 4c > 85 Divide both sides by 4. 4 4 c > 21.25 Josh cannot sell 0.25 candle, so he needs to sell at least 22 candles, or more than 21 candles, to earn a profit.
- 7. Check It Out: Example 3 It cost the class $15 to make cookies for the bake sale. How many cookies must they sell at 10¢ each to make a profit? Since profit is the amount earned minus the amount spent, the class needs to earn more than $15. Let c represent the number of cookies that must be sold. Write an inequality. 0.10c > 15 0.10c > 15 Divide both sides by .10. 0.10 0.10 c > 150 The class must sell more than 150 cookies to make a profit.
- 8. 1. It cost $730 to put on the school play. How many tickets must be sold at $6 a piece in order to make a profit? 6t > 730 t > 121.7 so at least 122 1. It cost Sophia $530 to make wind chimes. How many wind chimes must she sell at $12 apiece to make a profit? 12x > 530 x > 44.17 so at least 45
- 9. 3. It cost the Wilson children $55 to make lemonade. How many glasses must they sell at 75¢ each to make a profit? 0.75x > 55 x > 73.3 so at least 74 cups 4. Jorge’s soccer team is having its annual fund raiser. The team hopes to earn at least three times as much as it did last year. Last year the team earned $87. What is the team’s goal for this year? X > 87(3) x > 261 so at least $261
- 10. Class work Math book Pg. 132 # 7, 20, 21 Pg. 136 # 7, 20 , 21